How do I rotate an object with a image on it?
From what I understand your image is actually not part of the T-shirt material, it is an image plane that is shrinkwrapped around your T-shirt. So if you want to keep this solution, you need this plane to follow the T-shirt object. To do so, the simplest way is to parent the image to the T-shirt. If it doesn't give you satisfaction you should consider using the image as an Image Texture within the T-shirt material.